It has recently been pointed out by Kowalski et .
al .
( arxiv:0804.4142 ) that there is ‘ an unexpected brightness of the SnIa data at z > 1 ’ .
We quantify this statement by constructing a new statistic which is applicable directly on the Type Ia Supernova ( SnIa ) distance moduli .
This statistic is designed to pick up systematic brightness trends of SnIa datapoints with respect to a best fit cosmological model at high redshifts .
It is based on binning the normalized differences between the SnIa distance moduli and the corresponding best fit values in the context of a specific cosmological model ( eg \Lambda CDM ) .
These differences are normalized by the standard errors of the observed distance moduli .
We then focus on the highest redshift bin and extend its size towards lower redshifts until the Binned Normalized Difference ( BND ) changes sign ( crosses 0 ) at a redshift z _ { c } ( bin size N _ { c } ) .
The bin size N _ { c } of this crossing ( the statistical variable ) is then compared with the corresponding crossing bin size N _ { mc } for Monte Carlo data realizations based on the best fit model .
We find that the crossing bin size N _ { c } obtained from the Union08 and Gold06 data with respect to the best fit \Lambda CDM model is anomalously large compared to N _ { mc } of the corresponding Monte Carlo datasets obtained from the best fit \Lambda CDM in each case .
In particular , only 2.2 \% of the Monte Carlo \Lambda CDM datasets are consistent with the Gold06 value of N _ { c } while the corresponding probability for the Union08 value of N _ { c } is 5.3 \% .
Thus , according to this statistic , the probability that the high redshift brightness bias of the Union08 and Gold06 datasets is realized in the context of a ( w _ { 0 } ,w _ { 1 } ) = ( -1 , 0 ) model ( \Lambda CDM cosmology ) is less than 6 \% .
The corresponding realization probability in the context of a ( w _ { 0 } ,w _ { 1 } ) = ( -1.4 , 2 ) model is more than 30 \% for both the Union08 and the Gold06 datasets indicating a much better consistency for this model with respect to the BND statistic .